The family of the Indian gang-rape victim has spoken for the first time, calling for the men accused of the attack to be executed.

"The fight has just begun. We want all the accused hanged and we will fight for that, till the end," the brother of the 23-year-old medical student, who has not yet been named, told the Indian Express newspaper.

Hundreds of well-wishers, politicians and neighbours have crowded the family's modest home in south-west Delhi since the cremation of the victim's remains on Sunday morning.

The girl's mother was admitted to hospital after she collapsed following the funeral, local media reported.

"We are all in shock. Nobody can accept this news. My wife took it the hardest. It is too painful. I have not gone inside her room," her father said.

"She was born in this house. Her books, clothes they are all here. It is hard to believe I will never hear her voice again, she will never read books to me in English again."

The family has been held up as an example for the effort they made to fund the education of their daughter in a country where the schooling of male children is prioritised.

"While other kids cry before going to school, she would cry if we stopped her," the father , reported to be in his 50s, told the local DNA newspaper. "She was always keen on a career in medicine. She was most happy when she got a chance to heal somebody's wounds."